arXiv subjects

Abigail Timmel

Publications and source records attributed to Abigail Timmel.

7 recordsLinked to original sources

arXiv2026

Variational Monte Carlo Optimization of Topological Chiral Superconductors

We perform the variational Monte Carlo calculation for recently proposed chiral superconducting states driven by strong Coulomb interactions. We compare the resulting energetics of these electronic phases for the electron dispersion relation $E_k = c_2 k^2+c_4 k^4$. Motivated by the recent discovery of chiral superconductivity in rhombohedral graphene systems, we apply our analysis to relevant parameter regimes. We demonstrate that topological chiral superconducting phases (including a spin-unpolarized state) can be energetically favored over the spin-valley polarized Fermi liquid above the density of Wigner crystal phase. Our results show that the preference for chiral superconductivity is strongest when $c_2$ lies between zero and a negative value corresponding to a Fermi sea on the verge of forming a hole pocket around $k=0$. This finding suggests that superconductivity can arise from pure repulsive Coulomb interactions in systems with an almost flat band bottom, without relying on the pairing instability of a Fermi surface. This mechanism opens a new pathway to superconductivity beyond the conventional BCS mechanism.

cond-mat.str-el↗

arXiv2026

Non-Abelian Fibonacci quantum Hall states in 4-layer rhombohedral stacked graphene

In 1991, it was proposed that fourfold-degenerate Landau levels formed by a single species of electrons could host a non-Abelian fractional quantum Hall (FQH) state with Fibonacci anyons at filling fraction $ν= \frac{2}{3}$. In this work, we investigate how such degenerate Landau levels can be realized in rhombohedral-stacked tetralayer graphene. We identify the following key conditions which may stabilize the Fibonacci state: (1) A magnetic field of around 20 Tesla is required if surface and interior carbons have the same energy level. If substrate hybridization raises the surface carbon energy level by $Δ_2 = 30$\,meV relative to interior carbon, the required field will have a larger range: 15 -- 20 Tesla. For $Δ_2 = 45$\,meV, the range reaches a maximum: 7 -- 20 Tesla. (2) The displacement field must be tuned to achieve Landau level degeneracy. $ν= \frac{3}{5}$ Fibonacci FQH states may also be realized in pentalayer rhombohedral graphene with a magnetic field of 12 Tesla, and $ν= \frac12$ states with Ising anyons may occur in trilayer graphene for magnetic fields of 12 -- 20 Tesla at $Δ_2 = 0$ or 5 -- 20 Tesla at $Δ_2 = 45$\,meV. We also study a simple interaction model to explore spin/valley polarization effects, and we see that the Fibonacci statemay occur at $ν= 2/3 + $ integer filling fractions, where the integer is 0 and 4 for sufficiently weak interaction, or can shift to 2 and 5 under a stronger interaction. The case $Δ_2 = 45$\,meV also produces states at negative filling fraction, e.g. $-\frac23$, $-4\frac23$. Here $ν$ is defined with respect to the Hall conductance, $σ_{xy} = ν\frac{e^2}{h}$.

cond-mat.mes-hall↗

arXiv2025

Topological chiral superconductivity beyond pairing in a Fermi liquid

We investigate a mechanism to produce superconductivity by strong purely repulsive interactions for flat dispersion $\varepsilon \sim k^4$, without using pairing instability in Fermi-liquid. The resulting superconductors break both time-reversal and reflection symmetries in the orbital motion of electrons, and exhibit non-trivial topological order. Our findings suggest that this topological chiral superconductivity is more likely to emerge near or between fully spin-valley polarized metallic phase and Wigner crystal phase. These topological chiral superconductors can be fully or partially spin-valley polarized. For partial spin-valley polarization, the ratios of electron densities associated with different spin-valley quantum numbers are quantized as simple rational numbers. Furthermore, many of these topological chiral superconductors exhibit charge-4 or higher condensation, neutral quasiparticles with fractional statistics, and/or gapless chiral edge states. Two of the topological chiral superconductors are in the same phases as the ``spin''-triplet or spinless $p+ \textrm{i} p$ BCS superconductor, while others are in different phases than any BCS superconductors. The same mechanism is also used to produce anyon superconductivity between fractional anomalous quantum Hall states in the presence of a periodic potential.

cond-mat.str-el↗

arXiv2023

Quantum geometry beyond projective single bands

The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many geometrical concepts for single bands, the exploration of these concepts to a multi-band paradigm still promises a new field of interest. Formally, multi-band systems, featuring in particular degeneracies, have been related to projective spaces, explaining also the success of relating quantum geometrical aspects of flat band systems, albeit usually in the single band picture. Here, we propose a different route involving Plücker embeddings to represent arbitrary classifying spaces, being the essential objects that encode $all$ the relevant topology.This paradigm allows for the quantification of geometrical quantities directly in readily manageable vector spaces that a priori do not involve projectors or the need of flat band conditions. As a result, our findings are shown to pave the way for identifying new geometrical objects and defining metrics in arbitrary multi-band systems, especially beyond the single flatband limit, promising a versatile tool that can be applied in contexts that range from response theories to finding quantum volumes and bounds on superfluid densities as well as possible quantum computations.

cond-mat.mes-hall↗

arXiv2021

Anomalous Electrodynamics and Quantum Geometry in the Dirac-Harper model for a Graphene Bilayer

Graphene bilayers with layer antisymmetric strains are studied using the Dirac-Harper model for a pair of single layer Dirac Hamiltonians coupled by a one-dimensional moiré-periodic interlayer tunneling amplitude. This model hosts low energy, nearly dispersionless bands near charge neutrality that support anomalous polarizations of its charge multipole distributions. These are analyzed introducing a generalized Berry curvature that encodes the field-induced dynamics of multipole fields allowed in a chiral medium with time reversal symmetry. The formulation identifies a reciprocity relation between responses to layer-symmetric and layer-antisymmetric in-plane electric fields and reveals momentum-space quantum oscillations produced by a spatial pattern of band inversions on the moiré scale.

cond-mat.mes-hall↗

arXiv2020

Dirac-Harper Theory for One Dimensional Moiré Superlattices

We study a Dirac Harper model for moiré bilayer superlattices where layer antisymmetric strain periodically modulates the interlayer coupling between two honeycomb lattices in one spatial dimension. Discrete and continuum formulations of this model are analyzed. For sufficiently long moiré period the we find low energy spectra that host a manifold of weakly dispersive bands arising from a hierarchy of momentum and position dependent mass inversions. We analyze their charge distributions, mode count and valley-coherence using exact symmetries of the lattice model and approximate symmetries of a four-flavor version of the Jackiw-Rebbi one dimensional solution.

cond-mat.mes-hall↗

arXiv2018

Multiplication with Fourier Optics Simulating 16-bit Modular Multiplication

This paper will describe a simulator developed by the authors to explore the design of Fourier transform based multiplication using optics. Then it will demonstrate an application to the problem of constructing an all-optical modular multiplication circuit. That circuit implements a novel approximate version of the Montgomery multiplication algorithm that enables the calculation to be performed entirely in the analog domain. The results will be used to corroborate the feasibility of scaling the design up to 16-bits without the need for analog to digital conversions at intermediate steps.

eess.IV↗